Show that f and g are inverses of each other by verifying that f(g(x))=x=g(f(x)). f(x)=3x+2/x-1; g(x)= x+2/x-3

Question

basic concepts

Answer 1

Here is another way to approach the problem. One of the methods that you can verify if a function is an inverse of another function is to first look at the dependent variable f(x) and the independent variable x on one equation and then we switch the values where the f(x) becomes x and x becomes f(x)

 

Thus, you have the following

 

f(x) = (3x+2)/(x-1)

 

x= (3(f(x))+2)/(f(x)-1)

 

Then, we solve for f(x) 

 

x(f(x)-1) = (3f(x)+2) = x(f(x))-x

 

3f(x)-xf(x) = -x-2

 

(3-x)f(x) = -(x+2)

 

f(x) = (x+2)/(x-3) = g(x)

 

Please look at the process that I have shown you here. If you have any further questions, feel free to message me on Wyzant so that we can talk further.

Andy L.